Lattice

مشبك (Ar). Réseau (Fr). Gitter (Ge). Reticolo (It). 格子 (Ja). Решётка (Ru). Red (Sp).

A lattice in the vector space Vⁿ is the set of all integral linear combinations t = u₁a₁ + u₂a₂ + ... + u_ka_k of a system (a₁, a₂, ... , a_k) of linearly independent vectors in Vⁿ.

If k = n, i.e. if the linearly independent system is a basis of Vⁿ, the lattice is often called a full lattice. In crystallography, lattices are almost always full lattices, therefore the attribute 'full' is usually suppressed.

See also

• Crystallographic basis
• Crystal structure
• Chapters 1.3.2 and 3.1 of International Tables for Crystallography, Volume A, 6th edition